Question

Solve 4x+2 = 12 for x using the change of base formula

Answer 1

Answer:

x=2.5

Step-by-step explanation:

We have,

4x+2=12

\implies4x=10

Taking log both the sides we have,  

log\,4x=log\,10

\implies log\,4 + log\,x=log\,10 \left\:\: [ \because log\,ab = log\, a + log\, b\right ]

\implies log\,x=log\,10 -log\,4

\implies log\,x={ log\,(\frac{10}{4}) \:\:\left [\because log\,a -log\,b= log\,\frac{a}{b} \right ]

\implies log\,x=log\,2.5

\implies \frac{log\,x}{log\,2.5}=1

\implies log_{(2.5)}\, x=1\:\:\left [ \because log_{b}\,a=\frac{log\,a}{log\,b} \right ]

\implies x=(2.5)^{1}\:\: [ \because log_{b}\,a=m \implies a=b^{m} ]

Hence, we have x=2.5